Signal Space Expansion
An uncorrelated Rayleigh channel can be regarded as a worst case channel for digital radio communication. Crucial for the detection performance on this channel is the diversity order of the mobile communication system, which should be as large as possible. For trellis coded modulation (TCM) with symbol-interleaving the diversity order is the smallest number of distinct channel symbols along any error event. The diversity order can be further increased by bit-wise interleaving the encoder output before mapping the encoded data bits onto modulation symbols (see for example Ungerboeck, “Trellis-coded modulation with redundant signal sets Part I: Introduction” and “Trellis-coded modulation with redundant signal sets Part II: State of the art”, IEEE Communications Magazine, February 1987, Vol. 25, No. 2).
Signal space expansion generalized this concept of bit-interleaving such that a convolutional code of lower rate (larger Hamming distance) can be used giving an even higher diversity order. The same spectral efficiency is maintained by an expansion of the modulation symbol constellation. This concept is also commonly referred to as channel symbol expansion diversity (CSED).
Simulation results have indicated that this approach leads to coded modulation schemes experiencing a significantly better performance on the Rayleigh fading channel than the symbol- or bit-interleaved TCM-systems of comparable complexity.
Signal space (or Signal-Set) expansion thus allows avoiding spectral expansion of the transmitted data. For example in a coded system, k information bits are encoded into n coded bits prior to transmission. If this data is to be transmitted within a fixed time interval T, one approach is to expand the transmission bandwidth (or spectrum) by a factor of n/k compared to the transmission of the information bits only.
Alternatively—according to the approach taken by CSED—the transmission bandwidth is kept unchanged, but the number of data bits mapped to a modulation symbol is expanded by a factor of n/k. As an example, instead of transmitting an uncoded sequence of k bits using BPSK, a coded sequence of rate ½ may be used to transmit n=2 k bits using QPSK. Apparently both schemes require the same amount of symbols to be transmitted per time period for an identical data rate.
It should be apparent to those skilled in the art that an expansion can likewise occur to increase the amount of redundancy of a coded system even further. For example instead of transmitting a rate ⅔ system with 8-PSK, a signal space expansion scheme of rate 2/4 with 16-QAM may be used.
16-QAM
16-QAM (Quadrature Amplitude Modulation) is a digital modulation scheme which is commonly used for example in IMT 2000 based mobile communication systems, such as UMTS or CDMA 2000. The 16 modulation symbols are defined by distinct points in the complex signal space in which the 16-QAM constellation is commonly illustrated. Each of these points represents one 16-QAM symbol.
For binary information transmission systems, four different bits may be used to determine one of the existing 16-QAM symbols. Therefore one 16-QAM symbol consists (or can be represented by a word) of 4 bits, and is represented by a complex value in the complex plane. Generally the complex value of a modulation symbol can be represented by its Cartesian inphase- and quadrature-components (I and Q components) relative to the respective I-axis and Q-axis in the complex plane. These axes also divide the complex plane in four quadrants. The representation of a modulation symbol by its real and imaginary part in the complex plane is equivalent to its representation by polar components, i.e. radius and angle.
For a better understanding of the invention, it is assumed here a specific constellation of the 16-QAM symbols, where the signal points within a quadrant of the complex plane are arranged such that they form a square of four points in two orthogonal directions of the signal space. Consequently such a mapping is commonly known as square 16-QAM or lattice 16-QAM. Two examples are given in FIG. 1 and FIG. 2.
The invention assumes that the 16-QAM symbols are arranged using a square 16-QAM mapping. It should be apparent to the skilled person that for each rotated 16-QAM constellation as for example shown in FIG. 2, the axes of the complex plane may be chosen such that the rotated 16-QAM constellation can be viewed as in FIG. 1.
Commonly, the so-called Gray mapping is used to associate the 16 modulation symbols in a 16-QAM constellation with a quadruple of bits which is mapped to the respective symbol. According to this Gray mapping scheme, adjacent modulation symbols in the horizontal or vertical direction differ in one bit only.
Set Partitioning/Trellis Coded Modulation
Trellis-Coded Modulation (TCM) has evolved over the past decade as a combined coding and modulation technique for digital transmission over band-limited mobile communication channels. TCM allows significant coding gains over conventional uncoded modulation without compromising bandwidth efficiency (see for example Hansson et al., “Channel Symbol Expansion Diversity—Improved Coded Modulation for the Rayleigh Fading Channel”, IEEE International Conference on Communications, 1996 (ICC 96), Conference Record, Converging Technologies for Tomorrow's Applications. 1996, pages 891-895, vol. 2).
Trellis Coded Modulation (TCM) schemes employ redundant nonbinary modulation in combination with a finite-state encoder which governs the selection of modulation signals to generate coded signal sequences. A block diagram structure is given in FIG. 4. The essential concept of TCM is to use signal-set expansion to provide redundancy for coding, and to design coding and signal-mapping functions jointly so as to maximize directly the minimum Euclidean distance between coded signal sequences.
The concept of set partitioning is of central significance for TCM schemes. Set partitioning divides a signal set successively into smaller subsets with maximally increasing smallest intra-set distances.
TCM uses traditionally convolutional codes as coding schemes. An enhanced concept called Turbo Trellis Coded Modulation (TTCM) uses turbo codes as coding scheme.
Performance Evaluation
As shown in Ungeberboeck, “Trellis-coded modulation with redundant signal sets Part I: Introduction”, the resulting bit error rate of a signal coded and modulated according to a TCM scheme is improved in comparison to the uncoded transmission of the signal using a lower order modulation scheme.
However, the TCM is commonly not used in mobile communication systems, such as UMTS, since the encoder and in particular the decoder complexity required for TCM is very high. The complex structure of encoders and decoders for TCM require a not neglectable amount of processing power which in turn requires the presence of sufficient battery power in the terminal. As both resources are commonly scarce resources in mobile terminals, the use of TCM has not succeeded in mobile communications.
For example, TCM (signal space expansion) is not used in UMTS. Instead, signals are commonly modulated using QPSK or 16-QAM with Gray mapping (see 3GPP TS 25.213: “Spreading and modulation (FDD) (Release 6)”, V6.0.0, section 5.1, Table 3A, available at http://www.3gpp.org).